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Independent audit: correct QQ16 shear native-frame claim - #2252
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Prices the initial-prefix part of PR #2252's typed-fusion handoff. After factoring the common completed frame, PR #2216's paired A-to-T shear followed by B1's eight initial X_T inverse-line normalizations has, for each selected pair, the endpoint a' = a, t' = C_q^-1 (t + a), v' = v - C_q^-1 a. At payload characters 0 and 256 every actual q_T has bit 8 set, so each inverse line changes from 1 to -i; the difference of the two transfer matrices contains a 16-by-16 minor of determinant (-1-i)^16 = 256. Free payload-independent scalar gates have zero character difference and each single-field native line has difference rank at most one, so rank telescoping gives at least sixteen lines for any circuit in the model, even with scratch, copies and clears. A typed one-C0 prefix attains sixteen (eight more than inherited), restoring every borrowed helper and clearing C0. Fusion with later B1 operations or cover maps is outside the model; no supplier or kappa change. Adds research/qq16-shear-prefix-cost/ only. Submitted by @commdata2338 with substantial AI assistance (OpenAI Codex research and implementation; packaged with Claude Code). Co-Authored-By: Claude Opus 5.5 (1M context) <noreply@anthropic.com> Claude-Session: https://claude.ai/code/session_01X86sCSXdoDd61SDFfC1PKG
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PR #2216's sixteen-addition shear describes the F0/B1 boundary as a common data frame. The retained interface instead has
X_p: FandY_p: F C_q^-1. This package supplies exact counterexamples to applying its eightY_T -= X_Aupdates as bare native scalars on arbitrary payloads. The paired bare updates also fail to conserve the logical selected sum on these inputs.For a binary character with
q dot w = 1, bare subtraction writes-F chi_w; the intended result is-F C_q^-1 chi_w. At target 21 (q=289,w=1), their physical values at address zero are-iand-1. The proof applies to every selected target and every positive tensor length, under the inherited boundary convention. The verifier binds all eight targets to the frozen packet and literal F0/B1 wrappers.The contribution preserves #2216's reported rank-eight result on payload-constant inputs: all
C_qact as identity there. It does not replay that group-algebra calculation. A typed adaptation or fusion with B1 may still implement the logical shear; this audit proves no extra-child lower bound and claims no supplier or new kappa. Its practical purpose is to prevent an unrestricted controller from inheriting the sixteen-addition invoice without a typed implementation.Validation:
git diff --checkpass.One-command reproduction:
Expected:
PASS_QQ16_SHEAR_NATIVE_FRAME_AUDIT rejected_Y_adds=8 same_frame_X_updates=8 character_phases=4096 physical_vectors=8.The retained core boundary is inherited, not independently re-proved. This is not a full native traversal, hosting, or multiplication-theorem replay. No independent human review or formal-kernel proof is claimed. Base:
0fdd7d82de03e43c9e5a1000dfbcd380d1b687d2; audited #2216 head:b80e9ba43367fb8b20877a97da1cb677c34f9264.Credit Ali Romman and the retained QQ16 lineage for the construction and reviews, and Cinna Davis for the proposed shear. Prepared for Charles Bethin with substantial OpenAI Codex assistance. New material is Apache-2.0. The selected frontier and frozen predecessor files remain unchanged.